Erdős–Hajnal and VC-dimension (Tung Nguyen, Princeton)

Series
Combinatorics Seminar
Time
Friday, March 29, 2024 - 3:15pm for 1 hour (actually 50 minutes)
Location
Skiles 308
Speaker
Tung Nguyen – Princeton University – tunghn@math.princeton.eduhttps://web.math.princeton.edu/~tunghn/
Organizer
Evelyne Smith-Roberge

A hereditary class $\mathcal C$ of graphs is said to have the Erdős–Hajnal property if every $n$-vertex graph in $\mathcal C$ has a clique or stable set of size at least $n^c$. We discuss a proof of a conjecture of Chernikov–Starchenko–Thomas and Fox–Pach–Suk that for every $d\ge1$, the class of graphs of VC-dimension at most $d$ has the Erdős–Hajnal property. Joint work with Alex Scott and Paul Seymour.